Boltzmann’s Brain and Universe

One of the recent results of string theory is the revitalization of an old idea for the origin of the universe first proposed by Boltzmann.  This was nicely summarized in an article by Dennis Overbye in the New York Times. Cosmologist Sean Carroll has also blogged about this multiple times  (e.g. see here and here). Boltzmann suggested that the universe, which is not in thermal equilibrium, could have arisen as a fluctuation from a bigger universe in a state of thermal equilibrium.  (This involves issues of the second law of thermodynamics and the arrow of time, which I’ll post on at some later point.)  A paper by Dyson, Kleban and Susskind in 2002, set off a round of debates in the cosmology community because this idea leads to what is now called the Boltzmann’s brain paradox.  The details are nicely summarized in Carroll’s posts. Basically, the idea is that if a universe could arise out of a quantum fluctuation then a disembodied brain should also be able to pop into existence and since a brain is much smaller than the entire universe then it should be more probable.  So, why is it that we are not disembodied brains?

I had two thoughts when I first heard about this paradox.  The first was – how do you know you’re not a disembodied brain? and the second was –  it is not necessarily true that the brain is simpler than the whole universe.  What the cosmologists seem to be ignoring or discounting is nonlinear dynamics and computation.  The fact that the brain is contained in the universe  doesn’t mean it must be simpler.  They don’t take into account the possibility that the Kolmogorov complexity, which is the smallest description of an entity, of the universe is smaller than that of the brain.  So although the universe is much bigger than the brain and contains many brains among other things, it may in fact be less complex.  Personally, I happen to like the spontaneous fluctuation idea for the origin of our universe.

A simple example is to compare the number with a string of digits taken out of , e.g. the  th digit  to the th.   At face value, it would seem that the finite string of digits we selected would be more likely to arise than all of since it is smaller.  It’s like the proverbial monkeys typing would more likely produce the sentence “To be or not to be” than all of Hamlet.  However, the computational complexity of is probably smaller than our finite string because the algorithm to generate is shorter in bits than the string.  It is possible that there is a simpler algorithm to generate the string alone but that cannot be systematically deduced because  the Komogorov complexity is not computable. Hence, it would be more probable for random monkeys to type out the program to generate then a long string of digits embedded in .

This analogy also applies to fluctuations that create universes.  It could be that our universe has low Kolmogorov complexity so that it is much more likely for a fluctuation to arise that contains all of the laws of physics to dynamically generate a universe containing brains than it is to create a disembodied brain.   It would be the same as it being easier to write a program for a cellular automaton that spontaneously generates living organisms then it would be to write one that specifies all the details of that organism.  It may also be why AI is so difficult.  Reverse engineering the brain may be more difficult than reverse engineering the universe.  Someday, we may be able to grow artificial intelligences without ever really understanding how they work.  One could also argue that designing a brain through evolution is more likely than through creationism, but that is another debate.